Rational homotopy theory and differential forms
 Author/Creator
 Griffiths, Phillip, 1938 author.
 Language
 English.
 Edition
 Second edition.
 Publication
 New York : Birkhäuser, 2013.
 Physical description
 1 online resource.
 Series
 Progress in mathematics (Boston, Mass.) ; volume 16.
Access
Available online
More options
Contributors
 Contributor
 Morgan, John W., 1946 author.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Basic Concepts
 CW Homology Theorem
 The Whitehead Theorem and the Hurewicz Theorem
 Spectral Sequence of a Fibration
 Obstruction Theory
 EilenbergMacLane Spaces, Cohomology, and Principal Fibrations
 Postnikov Towers and Rational Homotopy Theory
 deRham's theorem for simplicial complexes
 Differential Graded Algebras
 Homotopy Theory of DGAs
 DGAs and Rational Homotopy Theory
 The Fundamental Group
 Examples and Computations
 Functorality
 The Hirsch Lemma
 Quillen's work on Rational Homotopy Theory
 A1structures and C1structures
 Exercises.
 Summary
 Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now The appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature. Zentralblatt MATH (Review of First Edition) The monograph is intended as an introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty of examples, illustrations, diagrams and exercises. The material is developed with patience and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and its power are elegantly presented. This is an excellent monograph. Bulletin of the American Mathematical Society (Review of First Edition) This completely revised and corrected version of the wellknown Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an indepth look at differential forms and de Thams theorem on simplical complexes. In addition, Sullivans results on computing the rational homotopy type from forms is presented.
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Phillip Griffiths, John Morgan.
 Series
 Progress in mathematics ; volume 16
 Available in another form
 Print version: Griffiths, Phillip, 1938 author. Rational homotopy theory and differential forms. Second edition 9781461484677 (OCoLC)857524732
 ISBN
 9781461484684
 1461484685